Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Average Error: 3.4 → 0.1

Time: 8.6s

Precision: binary64

Cost: 1352

Math

\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

↓

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+230}:\\ \;\;\;\;x - t_0 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 (- INFINITY))
     (* y (* z x))
     (if (<= t_0 5e+230) (- x (* t_0 x)) (* z (- (* y x) x))))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

↓

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y * (z * x);
	} else if (t_0 <= 5e+230) {
		tmp = x - (t_0 * x);
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z * x);
	} else if (t_0 <= 5e+230) {
		tmp = x - (t_0 * x);
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

↓

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y * (z * x)
	elif t_0 <= 5e+230:
		tmp = x - (t_0 * x)
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(y * Float64(z * x));
	elseif (t_0 <= 5e+230)
		tmp = Float64(x - Float64(t_0 * x));
	else
		tmp = Float64(z * Float64(Float64(y * x) - x));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = y * (z * x);
	elseif (t_0 <= 5e+230)
		tmp = x - (t_0 * x);
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+230], N[(x - N[(t$95$0 * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.4
Target	0.2
Herbie	0.1

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 64.0

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 0.3

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 5.0000000000000003e230

   1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Applied egg-rr 0.1

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x} \]

   if 5.0000000000000003e230 < (*.f64 (-.f64 1 y) z)

   1. Initial program 24.7

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Simplified 24.7

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(y, z, 1\right) - z\right)} \]
      Proof

      [Start] 24.7	\[ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
      *-commutative [=>] 24.7	\[ x \cdot \left(1 - \color{blue}{z \cdot \left(1 - y\right)}\right) \]
      sub-neg [=>] 24.7	\[ x \cdot \left(1 - z \cdot \color{blue}{\left(1 + \left(-y\right)\right)}\right) \]
      distribute-rgt-in [=>] 24.7	\[ x \cdot \left(1 - \color{blue}{\left(1 \cdot z + \left(-y\right) \cdot z\right)}\right) \]
      associate--r+ [=>] 24.7	\[ x \cdot \color{blue}{\left(\left(1 - 1 \cdot z\right) - \left(-y\right) \cdot z\right)} \]
      *-lft-identity [=>] 24.7	\[ x \cdot \left(\left(1 - \color{blue}{z}\right) - \left(-y\right) \cdot z\right) \]
      sub-neg [=>] 24.7	\[ x \cdot \left(\color{blue}{\left(1 + \left(-z\right)\right)} - \left(-y\right) \cdot z\right) \]
      distribute-lft-out-- [<=] 24.7	\[ \color{blue}{x \cdot \left(1 + \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right)} \]
      distribute-lft-in [=>] 24.7	\[ \color{blue}{\left(x \cdot 1 + x \cdot \left(-z\right)\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      *-rgt-identity [=>] 24.7	\[ \left(\color{blue}{x} + x \cdot \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right) \]
      +-commutative [=>] 24.7	\[ \color{blue}{\left(x \cdot \left(-z\right) + x\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      associate-+r- [<=] 24.7	\[ \color{blue}{x \cdot \left(-z\right) + \left(x - x \cdot \left(\left(-y\right) \cdot z\right)\right)} \]
      *-commutative [=>] 24.7	\[ x \cdot \left(-z\right) + \left(x - \color{blue}{\left(\left(-y\right) \cdot z\right) \cdot x}\right) \]
      cancel-sign-sub-inv [=>] 24.7	\[ x \cdot \left(-z\right) + \color{blue}{\left(x + \left(-\left(-y\right) \cdot z\right) \cdot x\right)} \]
      distribute-rgt-neg-in [=>] 24.7	\[ x \cdot \left(-z\right) + \left(x + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right)\right)} \cdot x\right) \]
      distribute-rgt1-in [=>] 24.7	\[ x \cdot \left(-z\right) + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right) + 1\right) \cdot x} \]
      *-commutative [=>] 24.7	\[ x \cdot \left(-z\right) + \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right)} \]
      +-commutative [=>] 24.7	\[ \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right) + x \cdot \left(-z\right)} \]

   3. Taylor expanded in z around inf 24.7

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in x around 0 0.4

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]

   5. Simplified 0.4

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - x\right)} \]
      Proof

      [Start] 0.4	\[ z \cdot \left(\left(y - 1\right) \cdot x\right) \]
      *-commutative [=>] 0.4	\[ z \cdot \color{blue}{\left(x \cdot \left(y - 1\right)\right)} \]
      sub-neg [=>] 0.4	\[ z \cdot \left(x \cdot \color{blue}{\left(y + \left(-1\right)\right)}\right) \]
      metadata-eval [=>] 0.4	\[ z \cdot \left(x \cdot \left(y + \color{blue}{-1}\right)\right) \]
      distribute-rgt-in [=>] 0.4	\[ z \cdot \color{blue}{\left(y \cdot x + -1 \cdot x\right)} \]
      mul-1-neg [=>] 0.4	\[ z \cdot \left(y \cdot x + \color{blue}{\left(-x\right)}\right) \]
      unsub-neg [=>] 0.4	\[ z \cdot \color{blue}{\left(y \cdot x - x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+230}:\\ \;\;\;\;x - \left(\left(1 - y\right) \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.1
Cost	1352

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternative 2
Error	4.4
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5.3 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3
Error	1.0
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -0.98 \lor \neg \left(z \leq 1.02 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 4
Error	19.6
Cost	652

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	19.6
Cost	652

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	11.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+85} \lor \neg \left(y \leq 1.86 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7
Error	19.5
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.5 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	33.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023016 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))